Finite Group Databasebeta

← #14789022

Subgroups — #14789022

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2#13078088C212yesmaximal, complemented
3C2×#10622674C212yesmaximal, complemented
4#13069840C212yesmaximal, complemented
5#13069662C212yesmaximal, complemented
6#13069448C212yesmaximal, complemented
7#13068608C211yesmaximal, characteristic, complemented
8#13068569C212yesmaximal, complemented
9C11×#2326C211yesmaximal, characteristic, complemented
10C2×#67037C2212yes—
11C2×C11×#124C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic, complemented
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66995C2214yescomplemented
15C2×#66983—22no—
16#10623086—22no—
17#10623085—24no—
18D4×D44—22no—
19#10623041C2212yes—
20#10623024—22no—
21#10623008C2212yes—
22C11×#391C2211yescharacteristic, complemented
23C11×#390C2211yescharacteristic
24C11×#388—22no—
25C11×#385—22no—
26C11×#384C2211yescharacteristic, complemented
27C11×#376C2211yescharacteristic, complemented
28C2×#66897C2212yes—
29#10622674—28no—
30#10622644—22no—
31#10622641—24no—
32#10622640—22no—
33#10622579C2214yescomplemented
34C2×#66869C2214yescomplemented
35C2×#66869C2214yescomplemented
36#10622537C2212yescomplemented
37#10622168C2212yescomplemented
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11D412yes—
41C22×C22⋊D11—24no—
42#67037—24no—
43#67037—24no—
44#67037—44no—
45C2×#4341—24no—
46C2×D4×D11—24no—
47C2×#4339C2314yes—
48C22×D44—22no—
49C11×#124—22no—
50C11×#124D414yescomplemented
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×#4326—24no—
67#66995—28no—
68#66995—44no—
69C2×#4325—24no—
70#66983—24no—
71#66983—24no—
72#66983—22no—
73#66983—22no—
74#66983—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×C4⋊Dic11—22no—
77C2×#4318C2314yes—
78#66950—24no—
79#66948—24no—
80#66939—28no—
81#66935—28no—
82#66928D414yes—
83#66927D412yes—
84C4×D44—22no—
85C4×D44—22no—
86#66922D412yes—
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—22no—
90#66897—24no—
91#66874—24no—
92#66873—24no—
93#66869—28no—
94#66869—44no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24228—111nomaximal, Sylow
98C24×C11C2×D412yes—
99C23×D11—24no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C2×D412yescomplemented
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C2×D412yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—82no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—48no—
122C2×C22⋊D11—48no—
123C22×Dic11—24no—
124#4341—48no—
125#4341—48no—
126D4×D11—48no—
127D4×D11—48no—
128#4339—24no—
129#4339—24no—
130#4339—24no—
131#4339—24no—
132C2×D44—24no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—84no—
136C2×D44C2×D414yes—
137C2×C4×D11—24no—
138C2×Dic22C2×D414yes—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—82no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—82no—
147C42×C11—21no—
148C42×C11—22no—
149C42×C11—42no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152C42×C11C2×D412yescomplemented
153#4326—48no—
154#4325—48no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161#4318—24no—
162#4318—24no—
163C2×C11⋊C8—24no—
164#3496—111no—
165#3037—112no—
166C2×#455—112no—
167#2326D1111yescharacteristic, complemented
168#2039—112no—
169#2007—112no—
170#1963—112no—
171#1800—111no—
172#1792—112no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11#12114yes—
178C23×C11C22×D411yescharacteristic
179C22×D11—24no—
180C22×D11—48no—
181C22×D11—84no—
182C22×D11—84no—
183Q8×C11—24no—
184Q8×C11—42no—
185D4×C11—24no—
186D4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—44no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12012yes—
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D412yes—
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)12yes—
211C22⋊D11—416no—
212C22⋊D11—44no—
213C22⋊D11—44no—
214C2×Dic11—24no—
215C2×Dic11—48no—
216D44—24no—
217D44—24no—
218D44—44no—
219D44—82no—
220D44—84no—
221C4×D11—44no—
222C4×D11—44no—
223Dic22—24no—
224Dic22—24no—
225C11⋊C8—44no—
226C2×H(5,𝔽2)—112no—
227C2×#137—114no—
228#547—222no—
229#546—224no—
230D42—222no—
231#537—112no—
232#534—222no—
233#532—112no—
234C2×#124C2×D1111yescharacteristic
235C2×#121—222no—
236C2×C4×Q8C2×D1111yescharacteristic, complemented
237C2×C4×D4C2×D1111yescharacteristic
238#464—224no—
239#462—222no—
240#460—222no—
241#455—228no—
242#423—112no—
243C2×#104—114no—
244C2×#104—114no—
245#417—114no—
246C2×#100—112no—
247#391C2×D1111yescharacteristic, complemented
248#390C2×D1111yescharacteristic
249#388—22no—
250#385—22no—
251#384C2×D1111yescharacteristic, complemented
252#376C2×D1111yescharacteristic, complemented
253#343—112no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—24no—
257C22×C11—44no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—82no—
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×#12111yescharacteristic
263C22×C11#53511yescharacteristic
264C2×D11—44no—
265C2×D11—44no—
266C2×D11—44no—
267C2×D11—168no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11D4212yes—
277C4×C11#54612yes—
278Dic11—44no—
279H(5,𝔽2)—224no—
280H(5,𝔽2)—224no—
281H(5,𝔽2)—444no—
282C2×#41—114no—
283C2×#41—224no—
284C22×Q8C22×D1111yescharacteristic
285C22×D4—222no—
286C22×D4—224no—
287C22×D4—224no—
288C22×D4C22×D1111yescharacteristic
289C23×C4C22⋊D1112yes—
290#137—228no—
291#137—444no—
292C2×Q16—224no—
293C2×SD16—224no—
294C2×M16—114no—
295C4⋊Q8—112no—
296#127—112no—
297#124—22no—
298#124—114no—
299#124D4414yescomplemented
300#123—228no—
301C22⋊Q8—224no—
302#121—224no—
303#121—224no—
304#121—224no—
305#121—222no—
306#121—224no—
307#121—222no—
308#120—228no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—222no—
314C4×D4—222no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—224no—
323C2×C22⋊C4C22⋊D1112yes—
324C2×C42—21no—
325C2×C42C22×D1111yescharacteristic
326C2×C42C22×D1111yescharacteristic
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—222no—
329C4⋊C8—222no—
330#104—228no—
331#104—444no—
332#103—224no—
333#102—224no—
334#100—224no—
335#95—21no—
336#95—21no—
337#95—22no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—44no—
341C2×C11#240811yescharacteristic
342C2×C11#301911yescharacteristic
343C2×C11#302211yescharacteristic
344D11—84no—
345C24—224no—
346C24C2×C22⋊D1112yes—
347#41—224no—
348#41—224no—
349#41—224no—
350#41—224no—
351#41—448no—
352#41—448no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—114no—
357C2×Q8C2×D4412yescomplemented
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—114no—
361C2×D4—224no—
362C2×D4—228no—
363C2×D4—224no—
364C2×D4—222no—
365C2×D4—222no—
366C2×D4—448no—
367C2×D4—448no—
368C2×D4—448no—
369C2×D4—448no—
370C2×D4—884no—
371C2×D4C2×D4412yes—
372C2×D4#433912yes—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—82no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C23×D1111yescharacteristic
386Q16—448no—
387SD16—448no—
388M16—224no—
389M16—224no—
390C2×C8—224no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—82no—
396C4⋊C4—224no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C22⋊C4—28no—
400C22⋊C4—24no—
401C22⋊C4—82no—
402C22⋊C4—228no—
403C22⋊C4—224no—
404C22⋊C4—224no—
405C42—21no—
406C42—22no—
407C42—42no—
408C42C2×D4412yescomplemented
409C42D4×D1112yes—
410C42D4×D1112yes—
411C11#2422811yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—42no—
415C23—42no—
416C23—224no—
417C23—448no—
418C23—884no—
419C23—884no—
420C23#6698314yes—
421C23C22×C22⋊D1111yescharacteristic
422Q8—24no—
423Q8—42no—
424Q8—224no—
425Q8—224no—
426D4—24no—
427D4—24no—
428D4—224no—
429D4—224no—
430D4—444no—
431D4—4416no—
432D4—444no—
433D4—444no—
434D4—882no—
435D4—884no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—82no—
453C2×C4—224no—
454C2×C4—448no—
455C2×C4—444no—
456C2×C4—444no—
457C2×C4#6699012yes—
458C2×C4#6699011yescharacteristic
459C2×C4#6699011yescharacteristic
460C2×C4C22×D4411yescharacteristic
461C2×C4C2×#433911yescharacteristic
462C2×C4C2×D4×D1112yes—
463C2×C4#6704212yes—
464C8—444no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—44no—
469C22—42no—
470C22—42no—
471C22—82no—
472C22—444no—
473C22—444no—
474C22—444no—
475C22—1768no—
476C22C2×#6698311yescharacteristic
477C22C2×#6699011yescharacteristic
478C22#1062336111yescharacteristic
479C4—21no—
480C4—21no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—444no—
488C4D4×D4412yes—
489C4#1062308112yes—
490C2—21no—
491C2—21no—
492C2—44no—
493C2—884no—
494C2#1307197211yescharacteristic
495C2#1307797211yescharacteristic
496C2#1307799411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2326D11
hypocenterC11#24228
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2326

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13078088C2semidirect
3. C2×#10622674C2semidirect
4. #13069840C2semidirect
5. #13069662C2semidirect
6. #13069448C2semidirect
7. #13068608C2semidirect
8. #13068569C2semidirect
9. C11×#2326C2semidirect
12. C2×C4×Q8×C11C22semidirect
14. C2×#66995C22semidirect
22. C11×#391C22semidirect
26. C11×#384C22semidirect
27. C11×#376C22semidirect
33. #10622579C22semidirect
34. C2×#66869C22semidirect
35. C2×#66869C22semidirect
36. #10622537C22semidirect
37. #10622168C22semidirect
50. C11×#124D4semidirect
103. C2×Q8×C11C2×D4semidirect
152. C42×C11C2×D4semidirect
167. #2326D11semidirect
236. C2×C4×Q8C2×D11semidirect
247. #391C2×D11semidirect
251. #384C2×D11semidirect
252. #376C2×D11semidirect
299. #124D44semidirect
357. C2×Q8C2×D44semidirect
408. C42C2×D44semidirect
411. C11#24228semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130823802
#130780882
C2×#106226742
#130698402
#130696622
#130694482
#130686082
#130685692
C11×#23262
#2422811